Separated by Track, Middle Distance, and Long Distance

For comparing pace by distance I look at each distance by its common grouping. The track world records are what I consider to be sprints, which are the 100 through 800 meters. I also add the 300 meters and 60 meters in this part since it is a somewhat significant event, and useful for analyzing pace decline rate. The arbitrary distance of one lap of a track being 400 meters likely does have an impact on which world records are best since all training is conducted on that basis, and hardly anyone targets training for 3/4ths of a lap. I consider these to be sprints because their pace is consistently above 20 miles per hour other than the 800 meters which can’t really be considered middle distance. By pace Usain Bolt’s 200 meters seems pretty crazy given how little it fell off compared to his 100 meter world record, but that seems like the nature of short distance sprinting, the start is what really matters in the 100 meters, look at the current world champion Christian Coleman for more evidence of that. The 60 meters world record pace is actually slower than the 300 meter world record! It seems that it is really hard for humans to get moving. A plot/animation of the speed of sprinters over the course of the race would be very interesting to see.

Next we have the “middle distance records”, which are some of the longest standing records in athletics, other than the 5000 meters which was just broken after 17 years by Joshua Cheptegei, the other records have stood in excess of 20 years, in spite of technological improvements in one of the most straightforward venues of athleticism. These records paces are also plotted in kilometers per hour (kmph). Hicham el Guerrouj and Daniel Komen’s records seem almost unbreakable, and el Guerrouj’s dominance across the lower middle distance world is truly astonishing.

Finally we have the long distance world records by time and pace, two things stand out right away, Gebrselassie and Moses’ world records are set to go, and pace decreases very slowly at this point. Humans are remarkably capable of maintaining a pace over long distances, once again acceleration over time would be great to see, for long distance runners I imagine it would be flat at 0 up until the final few kilometers.

Decomposing each of these distances into the three groups allows us to autocorrelate from an intercept of 0 and see the rate of time trend increase. I filter out Moses and Gebrselassie’s record since they are clearly ready to be beaten, they just haven’t been attempted at that distance yet. We see that at longer distances the rate of increase is actually lesser, which is to be expected since it takes less effort to maintain lower paces. To have any real meaning to this data a lot more would be needed as can be seen from the ridiculously high R^2 values. The formula by each group here is \(y = \beta_1*log(x) + \mu\), and the listed correlation coefficient therefore corresponds each 1% increase in distance to a y% increase in time. In the table of the model each one percent increase in distance by distance (short, middle, and long) results in a corresponding .007 minute, .065, and 0.66 minute increases. Significance isn’t really an issue here since the data for world records is necessarily limited to one per point, if there were more data on each line it would obviously be significant and since world record runners run at fairly even paces for every distance but the 100 meter if I added more data using similar times from similar distances and similar athletes, it would just fall along the already existing line. The long distance group predicts that a 1:55:22.9 marathon is possible, while the lower distance based models predict sub one hour marathons so those should definitely be entirely disregarded for longer distances.

Looking at all the world records I develop a quadratic-log-log model (\(y = \beta_0log(x)+\beta_1log(x)^2 + \mu\)) that predicts for each 1% increase in distance there is an expected 1.3% increase in time, and for each additional 1% there is a .013% decrease. This model indicates that the marathon world record, and half marathon world record have some room for improvement still as well, although it only predicts a 1:58:10.88 marathon.

Plotting Men’s and Women’s Current World Records Together

Men’s and Women’s Records with Pace

Percent Difference At Each Distance

By this metric it appears that the most impressive world records are the men’s 20,000 through 30,000 meters. This could also just be the result of these races being largely unimportant in the racing world, as evidenced by the jump in the ratio of the half marathon.

Percent Improvement for World Record Each Time

Usain Bolt is absolutely bonkers good, no one else has ever made such an individual dent into the 100 meter world record.

Animation of 100 Meter Records Over Time

Which Records Have Improved the Most Since their Inception?

The Marathon has improved the most by far, but based on the nationality of its competitors that could just be due to initially limited international competition, the story of the 1904 St. Louis Marathon in which only 32 athletes from 4 nations competed, and two South Africans being chased a mile out of the race by dogs was not even the craziest thing to happen (Google this one trust me). I would love to get more data on things like the 200 meter record but I just can’t seem to find any, I’m sure Usain Bolt’s record would be far greater if the data went further back like with other records. Despite the arbitratiness of a “starting record” it is clear athletes have gotten far, far better with time, in every distance the original record holder would not even qualify given the time disparities.

Animation of Each World Record Over Time